Pith Number

pith:QXVDQTBA

pith:2016:QXVDQTBA7OGBRN2V6CZPWDYKDE

not attested not anchored not stored refs pending

Congruence subgroups from representations of the three-strand braid group

Joseph Ricci, Zhenghan Wang

arxiv:1611.05103 v1 · 2016-11-16 · math.QA · math.GT · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QXVDQTBA7OGBRN2V6CZPWDYKDE}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:58:27.971865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85ea384c20fb8c18b755f0b2fb0f0a190f1be76a86872d309854a2606c4e197d

Aliases

arxiv: 1611.05103 · arxiv_version: 1611.05103v1 · doi: 10.48550/arxiv.1611.05103 · pith_short_12: QXVDQTBA7OGB · pith_short_16: QXVDQTBA7OGBRN2V · pith_short_8: QXVDQTBA

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QXVDQTBA7OGBRN2V6CZPWDYKDE \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 85ea384c20fb8c18b755f0b2fb0f0a190f1be76a86872d309854a2606c4e197d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c527338381952e29bb9d8afc12588b12f6158672c14406a2fbf1f8de0f534041",
    "cross_cats_sorted": [
      "math.GT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2016-11-16T00:51:42Z",
    "title_canon_sha256": "a77033ac6737c4f497109c058811281e831598b8e46d78e44b2a5b32ab2734a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.05103",
    "kind": "arxiv",
    "version": 1
  }
}